Numerical Methods Contents - SAM

1 Computing with Matrices and Vectors
Useful links:
Matlab Online Documentation
MATLAB guide
MATLAB Primer
The implementation of most numerical algorithms relies on array type data structures modelling concepts
from linear algebra (matrices and vectors).
Related information can be found in [18, Ch. 1].
1.1 Notations
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1.1.1 Vectors
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Vectors = are n-tuples (n ∈ N) with components x i ∈ K, over field K ∈ {R, C}.
vector = one-dimensional array (of real/complex numbers)
Part I
Default in this lecture:
vectors = column vectors
⎛
⎝ x ⎞
1
. ⎠ ∈ K n ( )
x1 · · · x n
x n
column vector
vector space of column vectors with n components
row vector
✎ notation for column vectors: bold small roman letters, e.g. x,y,z
Systems of Equations
Initialization of vectors in MATLAB:
column vectors x = [1;2;3];
row vectors y = [1,2,3];
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Transposing:
{
column vector ↦→ row vector
row vector ↦→ column vector .
⎛
⎝ x ⎞T
⎛
1
. ⎠ = ( ) ( ) T
x 1 · · · x n , x1 · · · x n = ⎝ x ⎞
1
. ⎠
x n x n
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Transposing in MATLAB: x_T = x’;